California Freight Cleanup → Investigation M-3

Can a portfolio beat the hand-crafted option on health, equity, and cost all at once?

100-point frontier • 4/6 seeds envelope-robustly dominated • max deaths: 970 at $8.9B

The portfolio robustness analysis (Investigation 23) evaluated six hand-crafted options by collapsing health, equity, and cost into a single dollar number — which forces a hidden exchange rate between outcomes nobody has agreed on. This investigation refuses that collapse. We ran an evolutionary search across a continuous design space and computed the full Pareto frontier: the set of allocations where you genuinely can’t improve on all three dimensions at once, without picking winners and losers up front.

The decision

Scalarizing health, equity, and cost into a single monetized number forces an implicit exchange rate between DAC and non-DAC deaths—one that is never stated, and that CEC reviewers are unlikely to endorse as a hidden assumption. Investigation M-3 does not make that choice. The output is a Pareto frontier: the set of allocations from which no reallocation simultaneously improves all three objectives. The frontier shows policymakers the actual tradeoff without a model-chosen weighting.

Two questions drive the investigation: what allocation structure cannot be improved on all three dimensions simultaneously, and how many of the six Investigation 6-4 hand-crafted portfolios survive a continuous search?

Methodology

Surrogate objective model. A deterministic linear function of five design variables: wildfire reduction fraction, transport spend ($B), building spend ($B), indoor AQ spend ($B), and DTE retire flag. Deaths-per-dollar coefficients are calibrated live each run from upstream investigations:

Coefficient	Value	Source
transport_deaths_per_B	39.97	Investigation 1-1 (baseline−T2) / $2B
building_deaths_per_B	41.22	Investigation 1-2 (baseline−B2) / $2B
wildfire_deaths_per_unit	218.0	Investigation 4-3 5% Di+Krewski midpoint / 0.05
indoor_deaths_per_B	320.25	Inv 19 indoor Di+Krewski midpoint / $2B
DTE_deaths	3.10	CARB Stockton TIRCP (fixed)

Three objectives minimized simultaneously by NSGA-II (Deb et al. 2002, IEEE TEC, population 100, 80 generations, SBX crossover eta = 15, polynomial mutation eta = 20, seed 42):

f1 = −deaths avoided (maximize aggregate health)
f2 = −DAC-weighted deaths avoided (maximize equity benefit)
f3 = cost ($B) (minimize spend)

GP residual correction (Phase 2d). A Gaussian Process is fit on residuals between Investigation M-1 P50 deaths and the linear surrogate at 5 named-portfolio anchors (Matern ν = 1.5, ARD, log-marginal-likelihood −20.61). A second NSGA-II run optimizes against the GP-corrected objective; its frontier reports separately as gp_pareto.

Envelope-robust dominance (Phase 5c.7). For each Investigation 6-4 seed, 1,000 Monte Carlo draws sample residuals from the GP’s predictive Normal(μ,σ). A seed is “envelope-robustly dominated” iff some frontier point dominates it in ≥95% of draws.

Findings

NSGA-II Pareto frontier: cost vs deaths-avoided, DAC-share as color — Figure: NSGA-II 100-point Pareto frontier (health × equity × cost). Color encodes DAC share of deaths avoided. Gray × marks dominated Investigation 6-4 seed portfolios; red diamond marks seeds on or near the frontier. E_smart (×, dominated by 48 frontier points) and Q_nsga_2 (★, Investigation M-2 reference) are explicitly labeled. Indoor AQ investment drives both the high-equity and high-deaths corners.

48 frontier allocations beat the “smart” portfolio on health, equity, and cost at the same time

The deterministic linear frontier produces 48 of 100 Pareto points that simultaneously beat E_smart_2B on deaths avoided, DAC-weighted deaths, and cost. The best dominator gains 580 additional deaths avoided while spending $230M less. Under the GP-corrected frontier, 5 of 100 points dominate E_smart; 5 of 6 seeds are GP-mean-dominated.

4 of 6 original portfolios are beaten in over 95% of 1,000 uncertainty draws — robust to model error

B_transport_2B, C_wildfire, E_smart, and balanced_2B are all envelope-robustly dominated (P = 1.00 in 1,000 GP-residual MC draws). A_free_lunch is on or near the frontier (P = 0.52) because its $0 cost makes it hard to dominate on all three dimensions. The indoor_focus seed is also on or near the frontier (P = 0.78) because its indoor-AQ-heavy design is closest to the NSGA-discovered high-equity region.

Indoor air quality is the high-efficiency, high-equity lever the hand-crafted menu underweighted

The max-DAC-share corner of the frontier ($1.92B cost, DAC share 0.302) is driven by indoor AQ investment—a lever the Investigation 6-4 hand-crafted menu never fully explored. Indoor AQ deaths-per-dollar (320.25/B) is 8× higher than transport (39.97) or building (41.22), primarily through its high DAC share. A CEC proposal emphasizing disadvantaged community benefit should lead with this corner.

The max-benefit corner of the continuous design space

The max-deaths corner of the 100-point frontier achieves 970 deaths avoided at $8.9B—roughly 5.8× the 166 deaths of D_all_in_4B at $4B, driven by the indoor AQ and wildfire levers filling the continuous design space above the Investigation M-1 discrete menu’s ceiling.

NSGA-II vs Investigation 6-4: what the two investigations answer

Investigation M-3 and Investigation 6-4 answer different questions. Investigation M-3 optimizes a 3-objective vector (deaths, DAC-deaths, cost) with no VSL conversion and no Monte Carlo uncertainty. Investigation 6-4 optimizes a scalar net-benefit (deaths × VSL − cost) with full CRF-posterior MC and CVaR robustness. A frontier point that dominates E_smart here may not dominate it under Investigation 6-4’s MC net-benefit distribution or CVaR criterion. This is not a contradiction—it is a difference in what “dominates” means.

Caveats

Deterministic surrogate, not MC. Frontier is computed against point-estimate deaths-per-$B with no uncertainty propagation. The same design vector dominating E_smart here may not dominate under Investigation 6-4’s MC net-benefit distribution.
Linear spend model. Constant marginal returns are assumed. Real programs exhibit diminishing returns at scale, overstating high-spend allocations.
Indoor AQ coefficient calibrated live but still carries uncertainty. The current 320.25 deaths/$B (from Inv 19 Di+Krewski midpoint) is a significant improvement over the prior hardcoded 150 deaths/$B, but Inv 19 shows sha256 drift. Re-verify before publishing indoor AQ allocations.
NSGA-II result is stochastic. The 100-point frontier is one draw with seed 42. The 48-dominator count is stable across this run but has not been convergence-tested against larger populations or generation budgets.
GP correction is small-N (5 anchors). Predictions at design points far from the anchors revert to the linear surrogate plus inflated residual uncertainty. GP-corrected frontier results are informational, not primary.

Provenance

Item	SHA-256 (12-char)
results.json	`0f8801139ccb`
analysis.md	—
scenario.md	—
Upstream: Investigation 6-4 (portfolio robust)	investigations/23_portfolio-robust/latest/results.json	`cab2edc05333`
Upstream: Inv 19 (indoor AQ)	investigations/19_indoor-air/latest/results.json	`9496484b2d20`
Key reference	Deb et al. (2002), IEEE TEC—NSGA-II algorithm. pymoo library implementation.
Run timestamp	2026-05-04T07:48:02 pop=100 gen=80 seed=42 runtime ~34s